The Stamford Bridge hierarchy are considering the experienced Dutchman if Conte’s relationship with the London club completely breaks down.
Conte has admitted that his bags are packed after a season spent fighting battles with his Blues bosses.
And Van Gaal could be asked to step in on an interim basis if the Italian leaves.
Van Gaal, 66, is looking for a short-term job – and is desperate to have another crack at the Premier League after being axed by Manchester United in 2016, just a day after winning the FA Cup.
If Chelsea and Conte part company, LVG would offer a safe pair of hands until the end of the season, when the Blues would make a permanent appointment.
Van Gaal has said: “I’d be interested in a Premier League club where I’d have the chance to get one over on Manchester United.”
He missed out on taking Australia to the World Cup when they appointed fellow Dutchman Bert van Marwijk.
Meanwhile, the bad blood between Mourinho and Conte is because they both treat their clubs like family, Ray Wilkins has claimed.
Since arriving in the Premier League, the Special One has had running feuds with Arsene Wenger, Rafa Benitez and Andres Villas-Boas and imported his old emnity with Pep Guardiola from Madrid to Manchester.
But the biggest grudge match in the Premier League is now between the twice ex-Chelsea boss and the current head coach at Stamford Bridge.
Last season Mourinho looked like an ex-boyfriend looking back fondly on his former love in West London with Conte keen to show he is now the man at Stamford Bridge.
The rivalry escalated last month with the Manchester United boss referring to match-fixing allegations against Conte and the Italian dismissing the Portuguese multiple-winner as a “little man”.
The Chelsea coach also said he was looking forward to their Old Trafford showdown today.
But former Chelsea and Manchester United star Ray Wilkins said: “When you meet them they are both very nice human beings.
“What they do is protect their own. It is a bit like a family. You look after your kids. No-one else can have a go at your kids but you can. And this is what they do. That is the way it is unfortunately. That is the way they are.
“These two appear to get on the least well of all the big managers now in the Premier League.
Mourinho also antagonised Conte last season by claiming Chelsea were “a very good defensive team” and they would win the title with “counter-attack goals and set-pieces goals”.
It was the pot calling the kettle black – but there was also truth in the barb. Wilkins added: “I saw Chelsea against Barcelona – I thought Chelsea didn't get at them as they should have done.
"I see Sunday if Antonio goes the same way with the three smaller guys up front, I think they might be able to hit MU on the counter-attack and think that is the way Antonio will go.
"It is a difficult one to call. If I were Jose, I would go all guns blazing and go to blast Chelsea out of the water. I think Chelsea will not be beaten.”
“But you had Jose with Arsene a few years ago where they didn't quite hit it off. Managers look after their own – I think that is the way to manage as well.
"Anyone can have a pop at anybody but once they have a pop at yours, you will defend your own and that is what they do and they do it wonderfully well. I don't really see there is a problem – they will be okay on Sunday.”